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variants of this functions
Hypergeometric2F1




Mathematica Notation

Traditional Notation









Hypergeometric Functions > Hypergeometric2F1[a,b,c,z] > Specific values > For rational parameters with denominators 4 and fixed z > For fixed z and a=-7/2, b>=a > For fixed z and a=-7/2, b=-7/4





http://functions.wolfram.com/07.23.03.aby7.01









  


  








Input Form





Hypergeometric2F1[-(7/2), -(7/4), 3, z] == (1/(114345 Pi Sqrt[1 + Sqrt[1 - z]] z^2)) (Sqrt[2] (-2 (1 - z)^(1/4) (448 - 9072 z - 218160 z^2 - 237028 z^3 - 17556 z^4 + 693 z^5) EllipticE[(2 (-1 + Sqrt[1 - z]) (1 - z)^(1/4) + z)/ (2 z)] - 2 (1 - z)^(3/4) (448 - 9072 z - 218160 z^2 - 237028 z^3 - 17556 z^4 + 693 z^5) EllipticE[(2 (-1 + Sqrt[1 - z]) (1 - z)^(1/4) + z)/ (2 z)] + (448 - 9296 z + 15024 z^2 + 311204 z^3 + 163064 z^4 + 231 z^5) EllipticK[(2 (-1 + Sqrt[1 - z]) (1 - z)^(1/4) + z)/(2 z)] + (1 - z)^(1/4) (448 - 9072 z - 218160 z^2 - 237028 z^3 - 17556 z^4 + 693 z^5) EllipticK[(2 (-1 + Sqrt[1 - z]) (1 - z)^(1/4) + z)/(2 z)] + Sqrt[1 - z] (448 - 9072 z - 218160 z^2 - 237028 z^3 - 17556 z^4 + 693 z^5) EllipticK[(2 (-1 + Sqrt[1 - z]) (1 - z)^(1/4) + z)/(2 z)] + (1 - z)^(3/4) (448 - 9072 z - 218160 z^2 - 237028 z^3 - 17556 z^4 + 693 z^5) EllipticK[(2 (-1 + Sqrt[1 - z]) (1 - z)^(1/4) + z)/(2 z)]))








Standard Form





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MathML Form







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<apply> <plus /> <apply> <times /> <cn type='integer'> 693 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 5 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 17556 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 4 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 237028 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 3 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 218160 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 9072 </cn> <ci> z </ci> </apply> </apply> <cn type='integer'> 448 </cn> </apply> <apply> <ci> EllipticK </ci> <apply> <times /> <apply> <plus /> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <power /> <apply> <plus 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Rule Form





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Date Added to functions.wolfram.com (modification date)





2007-05-02